Covariate Adjustment for the Win Odds: Application to Cardiovascular Outcomes Trials

TL;DR

This paper develops a covariate adjustment method for the win odds in clinical trials, enhancing precision and power by leveraging a connection to the probabilistic index, with demonstrated benefits on synthetic and real trial data.

Contribution

It introduces a novel covariate adjustment approach for the win odds, expanding its applicability and improving statistical efficiency in clinical trial analysis.

Findings

Covariate adjustment increases power when baseline covariates are prognostic.

The method shows potential power gains on synthetic and real trial data.

Small sample sizes may experience slight inflation of type I error rate.

Abstract

Covariate adjustment can enhance precision and power in clinical trials, yet its application to the win odds remains unclear. The win odds is an extension of the win ratio that counts ties as half a win for the treatment and the control group, respectively. In their original form, both the win ratio and the win odds rely on comparing each individual from the treatment group to each individual from the control group in a pairwise manner, and count the number of wins, losses, and ties from these pairwise comparisons. A priori, it is not clear how covariate adjustment can be implemented for the win odds. To address this, we establish a connection between the win odds and the marginal probabilistic index, a measure for which covariate adjustment theory is well-developed. Using this connection, we show how covariate adjustment for the win odds is possible, leading to potentially more precise estimators and larger power as compared to the unadjusted win odds. We present the underlying theory for covariate adjustment for the win odds in an accessible way and apply the method on synthetic data based on the CANTOS trial (ClinicalTrials.gov identifier: NCT01327846) characteristics, on a subset of the HF-ACTION trial data (ClinicalTrials.gov identifier: NCT00047437), and on simulated data to study the operating characteristics of the method. We observe that there is indeed a potential gain in power when the win odds is adjusted for baseline covariates if the baseline covariates are prognostic for the outcome. This comes at the cost of a slight inflation of the type I error rate for small sample sizes.